you need to assign a threshold to the noise you may have in your received signal in which any amplitude above that threshold is considered pure received signal. the time difference between the first peak of the input signal and the first peak of the received signal which has crossed that threshold level is considered the time difference.

This is a good question with many possible answers.   In addition to the helpful answer given by @Alireza sepehri nezhad, there is a bit more to add.

A practical example of how to estimate the time delay between input and output signals is given in

https://www.researchgate.net/publication/274715363_Time_Delay_Estimation_between_two_Biosignals_using_System_Identification

and

https://www.researchgate.net/publication/252056935_System_identification_for_nonlinear_FOPDT_model_with_input-dependent_dead-time

Conference Paper Time Delay Estimation between two Biosignals using System Id...

Article System identification for nonlinear FOPDT model with input-d...

This is already well answered by 2 previous responses. I would add that possibly instead of a threshold level for response, an alternative is to model the interval between input signal and response with say a baseline and ramp signal of slope to be identified with respect to input. The result is a model fit over a short duration that uses different  delay values in a desired range. The correct delay will be the case that provides white residuals throughout the baseline-ramp window with zero mean.

This approach works better when input levels can have different amplitudes - in such cases a simple threshold crossing will always give false smaller delays for larger inputs. Fitting a model instead is equivalent to normalizing to input level.